Question: Simplify the following expression: $ z = -1 + \dfrac{9x - 1}{3x + 10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3x + 10}{3x + 10}$ $ \dfrac{-1}{1} \times \dfrac{3x + 10}{3x + 10} = \dfrac{-3x - 10}{3x + 10} $ Therefore $ z = \dfrac{-3x - 10}{3x + 10} + \dfrac{9x - 1}{3x + 10} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-3x - 10 + 9x - 1}{3x + 10} $ $z = \dfrac{6x - 11}{3x + 10}$